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Darkmoon Card: Wrath
|Darkmoon Card: Wrath|right|left}} |slot=Trinket |level=70 |sell= |ilvl=100 }} This is one of the four available Darkmoon Cards trinkets added with the Burning Crusade expansion. Darkmoon Card Darkmoon Cards are obtained by completing a set of eight cards (The relevant Ace plus 7 general cards, numbered 2 of X deck and up to 8 of X deck - like, for example, Four of Beasts). After obtaining the eight cards the player can create a Deck item by clicking and activating the Ace card. All the individual cards and the deck itself are BoE items and can be bought in the Auction House. Once you have the deck item, you can turn it in the Darkmoon Faire for your final Epic trinket. Effects on Critcial Strike Chance for Casters The crit benefits of this trinket are affected by the chance of the player to have a streak of non-crit hits. These streaks are less likely for players who already have a high crit chance. Also, the trinket itself, by increasing crit chance, progressively makes long non-crit streaks less likely. Streaks of Non-Crits In this example, resists will not be counted. A player with a 25% crit rate will be assumed to have a 75% non-crit hit rate. The chance of a non-crit hit streak of a certain length to occur can be found by carrying the non-crit chance to the power of the length of the streak. In other words: * chance of streak = xy (where x = non-crit chance and y = length of streak) Streaks without Trinket # of Casts Crit Chance Non-Crit Chance Chance of Non-Crit Streak 1 0.2500 0.7500 0.7500 2 0.2500 0.7500 0.5625 3 0.2500 0.7500 0.4219 4 0.2500 0.7500 0.3164 5 0.2500 0.7500 0.2373 6 0.2500 0.7500 0.1780 7 0.2500 0.7500 0.1335 8 0.2500 0.7500 0.1001 9 0.2500 0.7500 0.0751 10 0.2500 0.7500 0.0563 So with a 25% crit rate, the chance of having a streak of 10 non-crits is 5.63% Although each cast has a 75% of being non-crit, the percentages have a cumulative effect when looking specifically for a block (or streak) of 10 non-crits in a row. However, with the trinket, x in the above formula changes with each new non-crit in the streak, because the buff progressively increases the crit rate. So it works like this: Streaks with Trinket # of Casts Crit Chance Non-Crit Chance Chance of Non-Crit Streak 1 0.2500 0.7500 0.7500 2 0.2577 0.7423 0.5567 3 0.2654 0.7346 0.4090 4 0.2731 0.7269 0.2973 5 0.2808 0.7192 0.2138 6 0.2885 0.7115 0.1521 7 0.2962 0.7038 0.1071 8 0.3038 0.6962 0.0745 9 0.3115 0.6885 0.0513 10 0.3192 0.6808 0.0349 The new Chance of Non-Crit Streak is equal to new Non-Crit Chance times the previous Chance of Non-Crit Streak. The blue * yellow = green numbers demonstrate this formula. * 0.7269 * 0.4090 = 0.2973 * 0.6808 * 0.0513 = 0.0349 As you can see, players with a 25% crit rate can raise their crit rate to 32% if they have 10 non-crits in a row, but the chance of having 10 non-crits in a row is only 3.5% Its tempting to say 7% crit rate increase occurs 3.5% of the time, yielding 0.242% overall crit increase. However, with a 3 non-crit streak, crit rate is increased by 1.5%. There is a 40% chance for a 3 non-crit streak. So 1.5% increase 40% of the time yields 0.6% overall increase. Because the effect is cumulative over any streak, picking a certain streak and dividing the crit rate increase over the total number of casts would inaccurately reflect the contribution of the buff. Rating the effect of the trinket The significant effect of the trinket is in how it decreases the Chance of Non-Crit Streak. You can think of Chance of Non-Crit Streak as the opposite of crit chance over a given number of casts. For example, in the above chart, there is a 10.71% chance for a streak of 7 non-crits. That also means that there is a 89.29% chance that the streak will fail, that any one cast out of a block of 7 will crit. However, without the effect of the trinket, the streak chance is 13.35% for 7 casts. Without the trinket, there is an 86.65% chance the streak will fail. So the trinket has increased the chance of at least one crit in any seven casts by 2.64%. Even though the 7 charges would add 5.38% crit chance to the next cast, the unlikelyhood of getting 7 non-crits in a row balances that out. This includes the cumulative effect of the base crit rate and the trinket's increasing charges. In other words, the effect of the trinket can be expressed in terms of the difference between the likelyhood of non-crit streaks with and without the trinket. The following graph shows net crit chance increase caused by the trinket over a number of casts for players with different amounts of base crit. So, as an example from the graph, a player with a base crit rate of 15% will be about 6% less likely to have a string of 14 non-crits due to the trinket. That is to say, he will be 6% more likely to have any one cast crit out of a block of 14. As you can see, the more base crit you have, the less benefit you get from the trinket, because the likelyhood of long strings of non-crits is so low. Also, as you consider longer and longer streaks, the net benefit of the trinket actually begins to decrease. This is because the chance of one crit in say 18 or 20 casts is so high that any amount of crit increase is insignificant. Summary Since Darkmoon Card: Wrath increases a player's crit rate only while the player is not critting, it is reducing its chance to build charges while building charges. So even though at 7 charges the trinket increases crit rate by 5.38%, we have to balance that with the increasing unlikelyhood that the player will have 7 non-crits in a row, an unlikelyhood affected by base crit plus added crit from the trinket. Instead of looking flatly at crit increase, we can look at the difference in likelyhood of non-crit streaks between streaks affected by the trinket and streaks with only base crit. The difference in these is the increased chance that any one cast across the streak will crit. Interestingly, we found that the benefit of the trinket maxes out at a certain point, and that longer streaks of non-crits are so unlikely that the trinket adds little to the cumulative effect of the base crit rate. Using this difference as a yardstick for the trinket's effect, here are some results for various base crit rates: Net Benefit from Trinket for Different Base Crit Rates Base Crit Average Effect Maximum Effect 10% 4.9% crit increase 54% of the time 12.7% crit increase 10.2% of the time 15% 2.8% crit increase 49% of the time 6.7% crit increase 10% of the time 20% 1.5% crit increase 50% of the time 4% crit increase 9.4% of the time 25% 0.6% crit increase 56% of the time 2.6% crit increase 10.7% of the time 30% 0.5% crit increase 49% of the time 1.8% crit increase 10% of the time * Average Effect is the crit rate increase for streaks that have a ~50% chance of occurance * Maximum Effect is the largest difference in likelyhood of non-crit streaks caused by the trinket Raw Data Net Crit Increase from Trinket Chance of Non-Crit Streak (10% base) Crit Chance Increase Chance of Non-Crit Streak (15% base) Crit Chance Increase Chance of Non-Crit Streak (20% base) Crit Chance Increase # of casts w/o trinket with trinket w/o trinket with trinket w/o trinket with trinket 1 0.9000 0.9000 0.0000 0.8500 0.8500 0.0000 0.8000 0.8000 0.0000 2 0.8100 0.8031 0.0069 0.7225 0.7160 0.0065 0.6400 0.6338 0.0062 3 0.7290 0.7104 0.0186 0.6141 0.5976 0.0166 0.5120 0.4973 0.0147 4 0.6561 0.6230 0.0331 0.5220 0.4941 0.0279 0.4096 0.3864 0.0232 5 0.5905 0.5415 0.0490 0.4437 0.4048 0.0389 0.3277 0.2972 0.0305 6 0.5314 0.4665 0.0649 0.3771 0.3285 0.0486 0.2621 0.2263 0.0358 7 0.4783 0.3983 0.0799 0.3206 0.2641 0.0565 0.2097 0.1706 0.0391 8 0.4305 0.3371 0.0934 0.2725 0.2102 0.0622 0.1678 0.1273 0.0405 9 0.3874 0.2826 0.1048 0.2316 0.1658 0.0658 0.1342 0.0940 0.0402 10 0.3487 0.2348 0.1139 0.1969 0.1294 0.0674 0.1074 0.0687 0.0387 11 0.3138 0.1932 0.1206 0.1673 0.1001 0.0673 0.0859 0.0497 0.0362 12 0.2824 0.1576 0.1249 0.1422 0.0766 0.0657 0.0687 0.0355 0.0332 13 0.2542 0.1273 0.1269 0.1209 0.0580 0.0629 0.0550 0.0252 0.0298 14 0.2288 0.1018 0.1270 0.1028 0.0435 0.0592 0.0440 0.0176 0.0264 15 0.2059 0.0807 0.1252 0.0874 0.0323 0.0550 0.0352 0.0122 0.0230 16 0.1853 0.0633 0.1220 0.0743 0.0237 0.0505 0.0281 0.0083 0.0198 17 0.1668 0.0492 0.1176 0.0631 0.0173 0.0459 0.0225 0.0056 0.0169 18 0.1501 0.0378 0.1123 0.0536 0.0124 0.0412 0.0180 0.0038 0.0142 19 0.1351 0.0288 0.1063 0.0456 0.0088 0.0368 0.0144 0.0025 0.0119 20 0.1216 0.0217 0.0999 0.0388 0.0062 0.0325 0.0115 0.0016 0.0099 Net Crit Increase from Trinket (2) Chance of Non-Crit Streak (25% base) Crit Chance Increase Chance of Non-Crit Streak (30% base) Crit Chance Increase # of casts w/o trinket with trinket w/o trinket with trinket 1 0.7500 0.7500 0.0000 0.7000 0.7000 0.0000 2 0.5625 0.5567 0.0058 0.4900 0.4846 0.0054 3 0.4219 0.4090 0.0129 0.3430 0.3318 0.0112 4 0.3164 0.2973 0.0191 0.2401 0.2246 0.0155 5 0.2373 0.2138 0.0235 0.1681 0.1503 0.0178 6 0.1780 0.1521 0.0258 0.1176 0.0994 0.0182 7 0.1335 0.1071 0.0264 0.0824 0.0650 0.0173 8 0.1001 0.0745 0.0256 0.0576 0.0420 0.0156 9 0.0751 0.0513 0.0238 0.0404 0.0268 0.0135 10 0.0563 0.0349 0.0214 0.0282 0.0169 0.0113 11 0.0422 0.0235 0.0187 0.0198 0.0105 0.0092 12 0.0317 0.0156 0.0160 0.0138 0.0065 0.0074 13 0.0238 0.0103 0.0135 0.0097 0.0039 0.0057 14 0.0178 0.0067 0.0111 0.0068 0.0024 0.0044 15 0.0134 0.0043 0.0091 0.0047 0.0014 0.0033 16 0.0100 0.0027 0.0073 0.0033 0.0008 0.0025 17 0.0075 0.0017 0.0058 0.0023 0.0005 0.0019 18 0.0056 0.0011 0.0046 0.0016 0.0003 0.0014 19 0.0042 0.0006 0.0036 0.0011 0.0002 0.0010 20 0.0032 0.0004 0.0028 0.0008 0.0001 0.0007 External Links Wowhead Thottbot Allakhazam